the vault shown is in the shape of a cube if each side is 4y to the 4th power find the volume

Answer: To find the solution of a system of equations, we can either use substitution or elimination method.

For this system of equations, we can use the substitution method:

First, we solve one equation for one of the variables. For example, we can solve the first equation for y: y = -2x - 4

Then, we substitute this expression of y into the second equation and solve for x: 1/2x + 6 = -2x - 4

We can simplify this equation by adding 2x to both sides: 1/2x + 2x + 6 = -4

And then by adding 6 to both sides: 1/2x + 2x + 12 = 2

And then by multiplying both sides by 2: x + 4x + 24 = 4

And then by simplifying: 5x = -20

Finally, we find x = -4

Now that we have found x, we can substitute it back into one of the equations to find y:

y = -2(-4) - 4 = 8 - 4 = 4

So the solution of the system of equations is x = -4 and y = 4

We can check that this solution satisfies both equations.

Step-by-step explanation:

Answer:

135

Step-by-step explanation:

30÷2≡15

Case 1: a = 0; b = 0 --> Real Number

Case 2: a = 0; b ≠ 0 --> Non-Real Complex Number

Case 3: a ≠ 0; b = 0 --> Real Number

Case 4: a ≠ 0; b ≠ 0 --> Non-Real Complex Number

For each case, we can determine whether the expression a + bi represents a real number or a non-real complex number based on the values of a and b.

Case 1: a = 0; b = 0

In this case, both a and b are zero. The expression a + bi simplifies to 0 + 0i, which is equal to 0. Therefore, the expression represents a real number.

Case 2: a = 0; b ≠ 0

Here, a is zero, but b is nonzero. The expression a + bi becomes 0 + bi, where b is a nonzero real number multiplied by the imaginary unit i. Since the expression contains a nonzero imaginary part, it represents a non-real complex number.

Case 3: a ≠ 0; b = 0

In this case, a is nonzero, but b is zero. The expression a + bi simplifies to a + 0i, which is equal to a. As there is no imaginary part in the expression, it represents a real number.

Case 4: a ≠ 0; b ≠ 0

Here, both a and b are nonzero. The expression a + bi contains both a real part (a) and an imaginary part (bi). Thus, it represents a non-real complex number.

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Answer:

Step-by-step explanation:

A) Commission = 2450 shillings * 25 % = 2450 shillings * (25/100) = 2450 shillings * (0.25) = 612.50 shillings

Commission = 612.50 shillings

B) If the total sale is 2,450.00 shillings, after the seller gives buyers a 2% discount. We must re-enter the discount:

2,450.00 shillings = X - X * 2% = X - 0.02 X --->

------> 0.98 X = 2,450.00 shillings

------>X= 2,450.00 / 0.98

------> X = 2,500.00  shillings

NEW COMMISSION = 2,500.00 shillings * 25 % = 2,500.00 shillings *(25/100) =2,500.00 shillings * (0.25) = 625 shillings

NEW COMMISSION = 625 shillings

Answer:

xw-6x+3w-18

Step-by-step explanation:

By using FOIL, we can solve the equation

First, Outside, Inside, Last

xw-6x+3w-18

Answer:

\(xw-6x+3w-18\)

Step-by-step explanation:

=> (x+3)(w-6)

USING FOIL

=> \(xw-6x+3w-18\)

The amount invested at 3% is $400, the amount invested at 4% is $700, and the amount invested at 5% is $1000.

Let's assume the amount invested at 4% is x dollars.

According to the given information, the amount invested at 5% is $1000 more than the amount invested at 4%.

So, the amount invested at 5% is (x + $1000).

The total amount invested is the sum of the amounts invested at each rate, which is $2100.

Therefore, we can write the equation:

x + (x + $1000) + (amount invested at 3%) = $2100

Now, we can calculate the amount invested at 3%.

We subtract the sum of the amounts invested at 4% and 5% from the total investment:

(amount invested at 3%) = $2100 - (x + x + $1000) = $2100 - (2x + $1000)

Given that Elena receives $95 per year in simple interest from the investments, we can use the formula for simple interest:

Simple Interest = Principal × Interest Rate

The interest earned from the investment at 3% is (amount invested at 3%) × 0.03, the interest earned from the investment at 4% is (amount invested at 4%) × 0.04, and the interest earned from the investment at 5% is (amount invested at 5%) × 0.05.

According to the problem, the total interest earned is $95.

So we can write the equation:

(amount invested at 3%) × 0.03 + (amount invested at 4%) × 0.04 + (amount invested at 5%) × 0.05 = $95

Now we can substitute the expression for (amount invested at 3%) and solve for x.

Once we have the value of x, we can calculate the amounts invested at 3%, 4%, and 5% using the given information.

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Answer:

60 miles prh because that is the amount of speed it takes to get there

We want to calculate the following expression

To do this, we will use the following properties of exponentiation.

We given a non zero number a, we have the following property

In our case, we have a=4, b =0 anc c=-11. So we have

Now, to write this number with a positive exponent

The percentage will spend > $247/day is 50%, the percentage will spend > $350/day is 4%, and the percentage will spend between $360 to $400 per day is 96.4%.

Mean, μ = 247

Standard deviation, σ = 60

(a) Percentage will spend when X > 247

The formula for the z score is:

z score = ( X - μ ) / σ

z score = ( 247 - 247 ) / 60

z score = 0

Then the percentage will be spent when X > 247 is 0.5 or 50%.

(b) Percentage will spend X > 350

z score = ( X - μ ) / σ

z score = ( 350 - 247 ) / 60

z score = 1.7167

Then the percentage will be spent when X > 350 is 0.04 or 4%.

(c) Between 360 to 400 per day

360 < X < 400

So,

z₁ = ( 360 - 247 ) / 60

z₁ = 1.88

So, the percentage for X > 360 is 0.029828.

And;

z₂ = ( 400 - 247 ) / 60

z₂ = 2.55

So, the percentage for X < 400 is 0.99461.

Therefore, the percentage spend between 360 and 400 per day is:

= 0.99461 - 0.029828 = 0.964782 or 96.4%.

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Answer:

60 Feet =  18.288 Meters

Step-by-step explanation:

foot = 12 inch = 0.3048 m

0.3047 × 60

18.288 meters

The weight of each small box is 25 pounds while the weight of each large box is 45 pounds

We know that we can be able to find the mass of each type of box from the use of simultaneous equations. Al we need to do is to form two systems of equations. Let the weight of each small box be x and the weight of each large box be y then;

x + y = 70 ------ (1)

50x + 70y = 4000 ----- (2)

x = 70 - y ------ (3)

Substitute equation (3) into (2)

Then;

50(70 - y) + 70y = 4000

3500 - 50y + 70y = 4000

20y = 4000 - 3500

20 y = 500

y= 25

Then substitute y = 25 into equation (1)

x + 25 = 70

x = 70 - 25

x = 45

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Answer:

Z = 22.5, Y = 81, X = 26.7

Step-by-step explanation:

Using the lengths you do know compare them to the copy, the only two lengths available that are for the same side length are 33 and 22, divide them together and you get 1.5. Thats the scale factor. Everything else you can figure out by multiplying or dividing by this scale factor.

\(Z = (15)(1.5) = 22.5\\Y = (54)(1.5) = 81\\X = (40)/(1.5) = 26.7\)

Answer:

option 1 is correct .. triangle ABC is congruent to DEF..

Answer:

Hope this helps

Step-by-step explanation:

5) Since AB = BC, this means that  ∠1 = ∠2

this would mean that BD bisects ∠ABC

Line AD = DC, and BD intersects at the angle of ADC, meaning that

∠3 = ∠4

6) M must be the midpoint of AC as M is perpendicular to BD, making M the Midpoint of AC

Answer:20

Step-by-step explanation:this is wrong

Answer:

40

Step-by-step explanation:

subtract median of dogs and median of cats

Answer:

- 151 is the answers

Step-by-step explanation:

The sample mean percentage x is 62.3% and the sample standard deviation S is 8.08%.

To find the percentage of hospitals that provide at least some charity care, we need to use the given sample data.

(a) Using a calculator with mean and sample standard deviation keys, we can find the sample mean percentage x and the sample standard deviation S.

\(x = \frac{56.9 + 55.9 + 52.5 + 65.7 + 59.0 + 64.7 + 70.1 + 64.7 + 53.5 + 78.2}{10}\\\\ = 62.3% \\\\\\\\S = \sqrt{\frac{((56.9 - 62.3)^2 + (55.9 - 62.3)^2 + ... + (78.2 - 62.3)^2) }{ 9}}\\\\ = 8.08\%\)

Therefore, the sample mean percentage x is 62.3% and the sample standard deviation S is 8.08%.

(b) To find a 90% confidence interval for the population average u of the percentage of hospitals providing at least some charity care, we can use the formula:

\(CI = x \pm z*(S/sqrtn)\)

where CI is the confidence interval, x is the sample mean percentage, z is the z-score for the desired confidence level (90% in this case), S is the sample standard deviation, and n is the sample size (10 in this case).

From the z-table, the z-score for a 90% confidence level is 1.645.

Plugging in the values, we get:

CI = 62.3 ± 1.645*(8.08/sqrt(10)) = (55.5%, 69.1%)

Therefore, we can be 90% confident that the true population average percentage of hospitals providing at least some charity care is between 55.5% and 69.1%.

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The value of the function T(x) + U(x) is -6x^4  + 2x^3 + x^2 - 4x + 2

The functions are given as:

T(x)= -6x^4 + x^2 - 1

U(x) = 2x^3 - 4x + 3.

To find T(x)+U(x), we have:

T(x) + U(x) = -6x^4 + x^2 - 1 + 2x^3 - 4x + 3.

Evaluate the like terms

T(x) + U(x) = -6x^4  + 2x^3 + x^2 - 4x + 2

Hence, the value of the function T(x) + U(x) is -6x^4  + 2x^3 + x^2 - 4x + 2

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Answer: F

Step-by-step explanation:

Answer: correct answer is A

Step-by-step explanation:

Remember that the coordinates (−2,−5π3) tell us the radius r=−2 and the angle θ=−5π3. So the point should be on the circle labeled 2 and form an angle of −5π3 with the negative x-axis. Point A is the correct point.

The number of cups of flour required by Jed is 7 1/2 cups.

Jed is baking shortbread for a bake sale.

The recipe calls for flour = 1 1/4 cups

and butter = 1/2 stick

Jed uses 1 stick of butter in:

= 1 1/4 ÷ 1/2

= 5/4 × 2/1

= 10/4

Therefore, Jed will use 3 stick of butter in = 10/4 × 3

= 30/4

= 15/2

= 7 1/2

Jed needs 7 1/2  cups of flour if he uses 3 sticks of butter.

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Answer:

72

Step-by-step explanation:

Answer:

7/10 or 0.7

The probability of Sara NOT picking an orange is 7/10

Step-by-step explanation:

Given that the basket of fruit contains;

10 lemons,

1 pear,

6 oranges, and

3 apples

Total number of fruits N = 20

The probability of not picking orange P(O');

P(O') = 1 - P(O) ........1

P(O) = probability of picking orange

P(O) = number of orange/total number of fruits

P(O) = 6/20

Applying equation 1;

P(O') = 1 - 6/20

P(O') = 14/20 = 7/10

P(O') = 7/10 or 0.7

The six terms of the series 247 are 2, 2, 2, 2, 2, and 2.

To find the six terms of a series, we need to first understand what a series is. A series is defined as the sum of the terms of a sequence. A sequence is a set of numbers in a specific order.

Therefore, a series is a sum of terms from a sequence. There are different types of series, and they have different formulas for calculating their terms.In this case, we are required to find the six terms of the series 247. Since this is a finite series, we can use a formula to calculate the nth term of a finite series.

The formula is given as follows:Tn = a + (n - 1) dWhere Tn is the nth term of the series, a is the first term of the series, n is the number of terms in the series, and d is the common difference between the terms of the series.To find the six terms of the series 247, we need to know the value of a and d. In this case, we can see that the first term of the series is 2. Therefore, a = 2.

Since this is a constant series, we can see that the common difference between the terms is 0. Therefore, d = 0.Substituting these values in the formula, we get:T1 = a + (1 - 1) dT1 = 2 + 0T1 = 2T2 = a + (2 - 1) dT2 = 2 + 0T2 = 2T3 = a + (3 - 1) dT3 = 2 + 0T3 = 2T4 = a + (4 - 1) dT4 = 2 + 0T4 = 2T5 = a + (5 - 1) dT5 = 2 + 0T5 = 2T6 = a + (6 - 1) dT6 = 2 + 0T6 = 2.

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The ordered pair is a vertex of the rectangle’s image will be (-4, -1). Then the correct option is B.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the structure and/or location of the object.

From before the refers to the object's initial condition, and Picture, after transformation, refers to the object's ultimate structure and location.

Rotation does not change the shape and size of the geometry. But changes the orientation of the geometry.

The rectangle is in the first quadrant then the coordinate of the vertices of a rectangle will be positive (x, y).

The rectangle is rotated 180º counterclockwise about the origin.

The rectangle will be in the third quadrant then the coordinate of the vertices of the rectangle will be negative (-x, -y).

Thus, the ordered pair is a vertex of the rectangle’s image will be (-4, -1). Then the correct option is B.

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Answer:

it's 0.5

Step-by-step explanation:

The best estimate of the correlation coefficient for the data set is 0.5.

So, option c is the correct answer.

The correlation coefficient is a measure of how similar two datasets are acting.

The range of correlation coefficient is [-1, 1]

When the correlation coefficient comes out as -1, it means that both the datasets are negatively oppositely correlated. One data increases, and other data starts to decrease in the opposite direction.

When the correlation coefficient comes out below 0, values are negatively correlated.

If the correlation coefficient comes out as 0, that means both the data sets are uncorrelated with respect to how we compare them.

When the correlation coefficient comes out > 0, that means both datasets' values are positively correlated.

If the correlation coefficient comes out as 1, then the values grow exactly similarly, in the same direction.

The best estimate of the correlation coefficient for the data set is 0.5.

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Daniella: Were you thinking of perpendicular lines?

Ori: It seems like you've got the basic idea, but your definition could be more precise.

Kaori: Yes! Well done. Here, have a cookie. You've earned it.